# sqpt01.f - Man Page

TESTING/LIN/sqpt01.f

## Synopsis

### Functions/Subroutines

real function **sqpt01** (m, n, k, a, af, lda, tau, jpvt, work, lwork)**SQPT01**

## Function/Subroutine Documentation

### real function sqpt01 (integer m, integer n, integer k, real, dimension( lda, * ) a, real, dimension( lda, * ) af, integer lda, real, dimension( * ) tau, integer, dimension( * ) jpvt, real, dimension( lwork ) work, integer lwork)

**SQPT01**

**Purpose:**

SQPT01 tests the QR-factorization with pivoting of a matrix A. The array AF contains the (possibly partial) QR-factorization of A, where the upper triangle of AF(1:k,1:k) is a partial triangular factor, the entries below the diagonal in the first k columns are the Householder vectors, and the rest of AF contains a partially updated matrix. This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) ) where || . || is matrix one norm.

**Parameters***M*M is INTEGER The number of rows of the matrices A and AF.

*N*N is INTEGER The number of columns of the matrices A and AF.

*K*K is INTEGER The number of columns of AF that have been reduced to upper triangular form.

*A*A is REAL array, dimension (LDA, N) The original matrix A.

*AF*AF is REAL array, dimension (LDA,N) The (possibly partial) output of SGEQPF. The upper triangle of AF(1:k,1:k) is a partial triangular factor, the entries below the diagonal in the first k columns are the Householder vectors, and the rest of AF contains a partially updated matrix.

*LDA*LDA is INTEGER The leading dimension of the arrays A and AF.

*TAU*TAU is REAL array, dimension (K) Details of the Householder transformations as returned by SGEQPF.

*JPVT*JPVT is INTEGER array, dimension (N) Pivot information as returned by SGEQPF.

*WORK*WORK is REAL array, dimension (LWORK)

*LWORK*LWORK is INTEGER The length of the array WORK. LWORK >= M*N+N.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **119** of file **sqpt01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sqpt01(3) is an alias of sqpt01.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK